Introduction To Mathematical Proofs Second Edition

Author : Charles Roberts
Publisher : Chapman and Hall/CRC
Page : 0 pages
File Size : 44,8 Mb
Release : 2014-12-17
Category : Mathematics
ISBN : 1482246872

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Introduction to Mathematical Proofs, Second Edition by Charles Roberts Pdf

Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs. Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs. This new edition includes more than 125 new exercises in sections titled More Challenging Exercises. Also, numerous examples illustrate in detail how to write proofs and show how to solve problems. These examples can serve as models for students to emulate when solving exercises. Several biographical sketches and historical comments have been included to enrich and enliven the text. Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It prepares them to succeed in more advanced mathematics courses, such as abstract algebra and analysis.

Author : Nicholas A. Loehr
Publisher : CRC Press
Page : 483 pages
File Size : 41,5 Mb
Release : 2019-11-20
Category : Mathematics
ISBN : 9781000709803

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An Introduction to Mathematical Proofs by Nicholas A. Loehr Pdf

An Introduction to Mathematical Proofs presents fundamental material on logic, proof methods, set theory, number theory, relations, functions, cardinality, and the real number system. The text uses a methodical, detailed, and highly structured approach to proof techniques and related topics. No prerequisites are needed beyond high-school algebra. New material is presented in small chunks that are easy for beginners to digest. The author offers a friendly style without sacrificing mathematical rigor. Ideas are developed through motivating examples, precise definitions, carefully stated theorems, clear proofs, and a continual review of preceding topics. Features Study aids including section summaries and over 1100 exercises Careful coverage of individual proof-writing skills Proof annotations and structural outlines clarify tricky steps in proofs Thorough treatment of multiple quantifiers and their role in proofs Unified explanation of recursive definitions and induction proofs, with applications to greatest common divisors and prime factorizations About the Author: Nicholas A. Loehr is an associate professor of mathematics at Virginia Technical University. He has taught at College of William and Mary, United States Naval Academy, and University of Pennsylvania. He has won many teaching awards at three different schools. He has published over 50 journal articles. He also authored three other books for CRC Press, including Combinatorics, Second Edition, and Advanced Linear Algebra.

Author : Gary Chartrand,Albert D. Polimeni,Ping Zhang
Publisher : Pearson Educacion
Page : 400 pages
File Size : 53,9 Mb
Release : 2013
Category : Logic, Symbolic and mathematical
ISBN : 0321782518

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Mathematical Proofs by Gary Chartrand,Albert D. Polimeni,Ping Zhang Pdf

This book prepares students for the more abstract mathematics courses that follow calculus. The author introduces students to proof techniques, analyzing proofs, and writing proofs of their own. It also provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory.

Author : Larry Gerstein
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 47,6 Mb
Release : 2013-11-21
Category : Science
ISBN : 9781468467086

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Introduction · to Mathematical Structures and · Proofs by Larry Gerstein Pdf

This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.

Author : Charles Roberts
Publisher : CRC Press
Page : 406 pages
File Size : 42,8 Mb
Release : 2014-12-17
Category : Mathematics
ISBN : 9781482246889

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Introduction to Mathematical Proofs by Charles Roberts Pdf

Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs.Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural num

Author : Martin Aigner,Günter M. Ziegler
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 44,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662223437

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Proofs from THE BOOK by Martin Aigner,Günter M. Ziegler Pdf

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Author : Charles Roberts
Publisher : CRC Press
Page : 434 pages
File Size : 47,5 Mb
Release : 2009-06-24
Category : Mathematics
ISBN : 9781420069563

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Introduction to Mathematical Proofs by Charles Roberts Pdf

Shows How to Read & Write Mathematical ProofsIdeal Foundation for More Advanced Mathematics CoursesIntroduction to Mathematical Proofs: A Transition facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize theorem proving. It helps students develop the skills n

Author : Daniel J. Velleman
Publisher : Cambridge University Press
Page : 401 pages
File Size : 40,8 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9780521861243

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How to Prove It by Daniel J. Velleman Pdf

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

Author : Charles E. Roberts
Publisher : Unknown
Page : 0 pages
File Size : 49,8 Mb
Release : 2015
Category : Electronic
ISBN : OCLC:911016646

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Introduction to Mathematical Proofs by Charles E. Roberts Pdf

Author : John P. D'Angelo,Douglas Brent West
Publisher : Unknown
Page : 0 pages
File Size : 51,7 Mb
Release : 2018
Category : Mathematics
ISBN : 0134689577

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Mathematical Thinking by John P. D'Angelo,Douglas Brent West Pdf

For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics-skills vital for success throughout the upperclass mathematics curriculum. The text offers both discrete and continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques (including induction), applies them to easily-understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The stimulating exercises are acclaimed for their exceptional quality.

Author : Richard H. Hammack
Publisher : Unknown
Page : 314 pages
File Size : 53,7 Mb
Release : 2016-01-01
Category : Mathematics
ISBN : 0989472116

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Book of Proof by Richard H. Hammack Pdf

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 55,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461221302

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Proofs and Fundamentals by Ethan D. Bloch Pdf

The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.

Author : Andrew Wohlgemuth
Publisher : Courier Corporation
Page : 385 pages
File Size : 46,9 Mb
Release : 2014-06-10
Category : Mathematics
ISBN : 9780486141688

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Introduction to Proof in Abstract Mathematics by Andrew Wohlgemuth Pdf

The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.

Author : Eric Gossett
Publisher : John Wiley & Sons
Page : 932 pages
File Size : 40,7 Mb
Release : 2009-06-22
Category : Mathematics
ISBN : 9780470457931

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Discrete Mathematics with Proof by Eric Gossett Pdf

A Trusted Guide to Discrete Mathematics with Proof?Now in a Newly Revised Edition Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include: An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofs New sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distribution Important examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databases Numerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theorem Extensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercises Combinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics.

Author : Douglas Smith,Maurice Eggen,Richard St. Andre
Publisher : Cengage Learning
Page : 416 pages
File Size : 42,9 Mb
Release : 2010-06-01
Category : Mathematics
ISBN : 0495562025

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A Transition to Advanced Mathematics by Douglas Smith,Maurice Eggen,Richard St. Andre Pdf

A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.